Hi @oronzo_lezzi,
I think setting userName on variables-fetched as in below code will solve your issue
<script cam-script type="text/form-script">
inject([ '$rootScope', '$scope', function($rootScope, $scope) {
camForm.on('variables-fetched', function() {
$scope.userName = $rootScope.authentication.name;
});
}]);
</script>
https://docs.camunda.org/manual/7.12/reference/embedded-forms/lifecycle/
variables-fetched is fired after the request returns and the values of the variables have been merged into the variableManager.